Putting the R in phaRmacy
04/12/2020
All sites and drugs
Drug A
Site A
Seasonality
Week
Year
Raw data
Detail of data
Weekly totals
Detail of weekly totals
Residuals of STL model- raw data and weekly totals
Simple exponential smoothing
| .model | term | estimate |
|---|---|---|
| ETS(quantity ~ season(method = “N”)) | alpha | 0.0001002 |
| ETS(quantity ~ season(method = “N”)) | l | 162.3565708 |
Ljung Box test for autocorrelation of residuals
| .model | lb_stat | lb_pvalue |
|---|---|---|
| ETS(quantity ~ season(method = “N”)) | 17.63355 | 0.0614688 |
ARIMA
| .model | term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|---|
| ARIMA(quantity) | ar1 | 0.6160404 | 0.1679878 | 3.667174 | 0.0002858 |
| ARIMA(quantity) | ma1 | -0.6055922 | 0.1698636 | -3.565169 | 0.0004173 |
| ARIMA(quantity) | ma2 | 0.1340922 | 0.0598298 | 2.241227 | 0.0256759 |
| ARIMA(quantity) | sar1 | 0.0981877 | 0.0639542 | 1.535283 | 0.1256726 |
| ARIMA(quantity) | constant | 56.3162905 | 3.3440977 | 16.840504 | 0.0000000 |
Ljung Box test for autocorrelation of residuals
| .model | lb_stat | lb_pvalue |
|---|---|---|
| ARIMA(quantity) | 6.277749 | 0.7914132 |
Model testing
Weekly data
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE |
|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | -17.955 | 99.947 | 88.679 | -Inf | Inf | 0.71325 |
| ETS(quantity ~ season(method = “N”)) | Test | -10.876 | 104.840 | 91.000 | -Inf | Inf | 0.73192 |
| FASSTER(quantity ~ trend(1)) | Test | 45.033 | 113.580 | 91.000 | -Inf | Inf | 0.73192 |
| prophet(quantity) | Test | 12.226 | 105.350 | 101.280 | -Inf | Inf | 0.81459 |
| SNAIVE(quantity) | Test | -92.667 | 122.390 | 104.330 | -Inf | Inf | 0.83916 |
Daily data
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE |
|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | -1.0351 | 54.794 | 36.070 | -Inf | Inf | 1.05120 |
| ETS(quantity ~ season(method = “A”)) | Test | -1.9517 | 56.102 | 35.553 | -Inf | Inf | 1.03620 |
| FASSTER(quantity ~ trend(1) + fourier(7)) | Test | -17.4840 | 58.755 | 45.809 | -Inf | Inf | 1.33510 |
| prophet(quantity ~ season(7)) | Test | -2.5801 | 55.874 | 35.886 | NaN | Inf | 1.04580 |
| SNAIVE(quantity ~ lag(“week”)) | Test | -2.3333 | 57.196 | 25.667 | -Inf | Inf | 0.74802 |
Cross validation
Cross validated accuracy for a variety of models using weekly data.
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE | ACF1 |
|---|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | -12.8141644 | 124.7169 | 102.8665 | -Inf | Inf | 0.8375329 | -0.2324731 |
| ETS(quantity ~ season(method = “N”)) | Test | -4.5191525 | 123.5376 | 100.5418 | -Inf | Inf | 0.8186048 | -0.1909788 |
| FASSTER(quantity ~ trend(1)) | Test | -65.0342019 | 144.0960 | 123.1841 | -Inf | Inf | 1.0029574 | -0.0393517 |
| prophet(quantity) | Test | -5.5127510 | 140.7218 | 115.9168 | -Inf | Inf | 0.9437876 | 0.0352620 |
| SNAIVE(quantity) | Test | -0.1666667 | 166.2477 | 130.7917 | -Inf | Inf | 1.0648975 | 0.0135623 |
Cross validation- daily
Cross validated accuracy for a variety of models using daily data.
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE | ACF1 |
|---|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | -12.151161 | 38.60934 | 28.46236 | -Inf | Inf | 0.8242388 | -0.0531722 |
| ETS(quantity ~ season(method = “A”)) | Test | -15.265937 | 37.59509 | 28.07931 | -Inf | Inf | 0.8131461 | -0.0773882 |
| FASSTER(quantity ~ trend(1) + fourier(7)) | Test | 8.258277 | 35.16723 | 20.55201 | NaN | Inf | 0.5951637 | -0.0782716 |
| prophet(quantity ~ season(7)) | Test | -17.672399 | 38.66555 | 30.13475 | -Inf | Inf | 0.8726694 | -0.0839118 |
| SNAIVE(quantity ~ lag(“week”)) | Test | -5.333333 | 56.33235 | 25.33333 | -Inf | Inf | 0.7336256 | -0.0092600 |
Site B
Seasonality
Week
Year
Raw data
Detail of data
Weekly totals
Detail of weekly totals
Residuals of STL model- raw data and weekly totals
Simple exponential smoothing
| .model | term | estimate |
|---|---|---|
| ETS(quantity ~ season(method = “N”)) | alpha | 0.0001 |
| ETS(quantity ~ season(method = “N”)) | l | 2018.9770 |
Ljung Box test for autocorrelation of residuals
| .model | lb_stat | lb_pvalue |
|---|---|---|
| ETS(quantity ~ season(method = “N”)) | 271.4111 | 0 |
ARIMA
| .model | term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|---|
| ARIMA(quantity) | ma1 | -1.5644956 | 0.0443110 | -35.307164 | 0.0000000 |
| ARIMA(quantity) | ma2 | 0.5815256 | 0.0442398 | 13.144845 | 0.0000000 |
| ARIMA(quantity) | sma1 | 0.1117924 | 0.0564947 | 1.978812 | 0.0486708 |
Ljung Box test for autocorrelation of residuals
| .model | lb_stat | lb_pvalue |
|---|---|---|
| ARIMA(quantity) | 56.09459 | 0 |
Model testing
Weekly data
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE |
|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | -269.200 | 1095.30 | 815.82 | -74.093 | 93.163 | 1.3412 |
| ETS(quantity ~ season(method = “N”)) | Test | -237.780 | 908.66 | 722.17 | -61.588 | 78.739 | 1.1873 |
| FASSTER(quantity ~ trend(1)) | Test | -101.730 | 882.88 | 722.17 | -50.728 | 73.447 | 1.1873 |
| prophet(quantity) | Test | -191.960 | 921.73 | 739.09 | -60.481 | 81.026 | 1.2151 |
| SNAIVE(quantity) | Test | 10.833 | 1837.60 | 1650.20 | -83.329 | 150.260 | 2.7130 |
Daily data
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE |
|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | -36.0820 | 434.43 | 347.90 | -Inf | Inf | 0.96973 |
| ETS(quantity ~ season(method = “A”)) | Test | -8.8812 | 408.04 | 282.32 | NaN | Inf | 0.78695 |
| FASSTER(quantity ~ trend(1) + fourier(7)) | Test | 235.1800 | 531.75 | 379.76 | NaN | Inf | 1.05850 |
| prophet(quantity ~ season(7)) | Test | -5.4564 | 478.04 | 327.23 | NaN | Inf | 0.91214 |
| SNAIVE(quantity ~ lag(“week”)) | Test | 185.2100 | 479.98 | 262.02 | -Inf | Inf | 0.73037 |
Cross validation
Cross validated accuracy for a variety of models using weekly data.
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE | ACF1 |
|---|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | 141.9050 | 1119.897 | 935.5436 | -81.45248 | 116.5322 | 1.562056 | -0.3900158 |
| ETS(quantity ~ season(method = “N”)) | Test | 130.9735 | 1035.014 | 863.4654 | -84.11084 | 115.2071 | 1.441709 | -0.3069377 |
| FASSTER(quantity ~ trend(1)) | Test | 175.0720 | 1101.875 | 948.1003 | -80.17792 | 116.6875 | 1.583022 | -0.2019976 |
| prophet(quantity) | Test | 179.1003 | 1071.280 | 899.2753 | -85.09568 | 119.3850 | 1.501500 | -0.2554177 |
| SNAIVE(quantity) | Test | 190.6875 | 1307.670 | 1035.2292 | -69.98942 | 113.6331 | 1.728499 | -0.3973729 |
Cross validation- daily
Cross validated accuracy for a variety of models using daily data.
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE | ACF1 |
|---|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | -6.314599 | 514.8799 | 362.1752 | -Inf | Inf | 1.0099517 | -0.0644588 |
| ETS(quantity ~ season(method = “A”)) | Test | -32.049368 | 491.9708 | 336.1137 | -Inf | Inf | 0.9372774 | -0.0991452 |
| FASSTER(quantity ~ trend(1) + fourier(7)) | Test | -132.485406 | 513.9743 | 391.2897 | -Inf | Inf | 1.0911394 | -0.0873330 |
| prophet(quantity ~ season(7)) | Test | -12.180340 | 491.2121 | 322.2710 | NaN | Inf | 0.8986758 | -0.0957201 |
| SNAIVE(quantity ~ lag(“week”)) | Test | -148.500000 | 611.1046 | 437.1667 | -Inf | Inf | 1.2190708 | -0.2450742 |
Site C
Seasonality
Week
Year
Raw data
Detail of data
Weekly totals
Detail of weekly totals
Residuals of STL model- raw data and weekly totals
Simple exponential smoothing
| .model | term | estimate |
|---|---|---|
| ETS(quantity ~ season(method = “N”)) | alpha | 0.0001 |
| ETS(quantity ~ season(method = “N”)) | l | 3297.9622 |
Ljung Box test for autocorrelation of residuals
| .model | lb_stat | lb_pvalue |
|---|---|---|
| ETS(quantity ~ season(method = “N”)) | 159.7713 | 0 |
ARIMA
| .model | term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|---|
| ARIMA(quantity) | ma1 | -1.5802277 | 0.0421181 | -37.519010 | 0 |
| ARIMA(quantity) | ma2 | 0.6097934 | 0.0439426 | 13.877053 | 0 |
| ARIMA(quantity) | sma1 | 0.3502639 | 0.0583689 | 6.000861 | 0 |
Ljung Box test for autocorrelation of residuals
| .model | lb_stat | lb_pvalue |
|---|---|---|
| ARIMA(quantity) | 64.2106 | 0 |
Model testing
Weekly data
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE |
|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | -160.180 | 1592.4 | 1351.3 | -40.251 | 63.339 | 1.6235 |
| ETS(quantity ~ season(method = “N”)) | Test | 14.938 | 1447.0 | 1225.5 | -29.304 | 53.342 | 1.4723 |
| FASSTER(quantity ~ trend(1)) | Test | -183.680 | 1458.5 | 1291.7 | -37.091 | 58.562 | 1.5519 |
| prophet(quantity) | Test | 102.970 | 1472.1 | 1256.2 | -25.067 | 51.408 | 1.5093 |
| SNAIVE(quantity) | Test | 10.667 | 2195.8 | 1868.0 | -48.360 | 90.024 | 2.2443 |
Daily data
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE |
|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | -21.0540 | 707.47 | 528.15 | -Inf | Inf | 1.24260 |
| ETS(quantity ~ season(method = “A”)) | Test | -6.1685 | 653.88 | 438.91 | -Inf | Inf | 1.03260 |
| FASSTER(quantity ~ trend(1) + fourier(7)) | Test | 354.1400 | 728.82 | 461.54 | Inf | Inf | 1.08590 |
| prophet(quantity ~ season(7)) | Test | 9.1109 | 638.21 | 422.53 | NaN | Inf | 0.99407 |
| SNAIVE(quantity ~ lag(“week”)) | Test | 303.1900 | 724.97 | 387.52 | -40.53 | 142.2 | 0.91172 |
Cross validation
Cross validated accuracy for a variety of models using weekly data.
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE | ACF1 |
|---|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | 101.68153 | 1070.105 | 878.7796 | -15.151884 | 38.97492 | 1.068348 | -0.5428149 |
| ETS(quantity ~ season(method = “N”)) | Test | 27.84641 | 1073.538 | 864.4255 | -19.045617 | 40.06804 | 1.050897 | -0.4386608 |
| FASSTER(quantity ~ trend(1)) | Test | 211.68458 | 1216.285 | 1029.0467 | -13.243619 | 43.34534 | 1.251030 | -0.1285904 |
| prophet(quantity) | Test | 255.93076 | 1132.394 | 972.9201 | -10.244049 | 39.91888 | 1.182796 | -0.3406090 |
| SNAIVE(quantity) | Test | 213.60417 | 1414.393 | 1084.1875 | -9.827629 | 42.51235 | 1.318065 | -0.5216012 |
Cross validation- daily
Cross validated accuracy for a variety of models using daily data.
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE | ACF1 |
|---|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | 62.90364 | 669.9151 | 489.9540 | -Inf | Inf | 1.1646896 | 0.0627889 |
| ETS(quantity ~ season(method = “A”)) | Test | 69.48203 | 626.7777 | 406.4979 | -Inf | Inf | 0.9663026 | -0.0031281 |
| FASSTER(quantity ~ trend(1) + fourier(7)) | Test | 164.92504 | 645.2205 | 428.8795 | NaN | Inf | 1.0195069 | -0.0123546 |
| prophet(quantity ~ season(7)) | Test | 87.19625 | 626.9062 | 410.7530 | NaN | Inf | 0.9764176 | -0.0117592 |
| SNAIVE(quantity ~ lag(“week”)) | Test | 86.45238 | 646.5062 | 365.5000 | -Inf | Inf | 0.8688448 | -0.2836529 |
Drug B
Drug B is excluded from this analysis because there is only 3 years of data for Drug B. It may be included at a later date.
Drug C
Site A
Seasonality
Week
Year
Raw data
Detail of data
Weekly totals
Detail of weekly totals
Residuals of STL model- raw data and weekly totals
Simple exponential smoothing
| .model | term | estimate |
|---|---|---|
| ETS(quantity ~ season(method = “N”)) | alpha | 0.0412606 |
| ETS(quantity ~ season(method = “N”)) | l | 0.2623830 |
Ljung Box test for autocorrelation of residuals
| .model | lb_stat | lb_pvalue |
|---|---|---|
| ETS(quantity ~ season(method = “N”)) | 17.77709 | 0.0588423 |
ARIMA
| .model | term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|---|
| ARIMA(quantity) | ar1 | -0.0701466 | 0.0586881 | -1.195245 | 0.2328629 |
| ARIMA(quantity) | ma1 | -0.9615223 | 0.0226335 | -42.482203 | 0.0000000 |
| ARIMA(quantity) | constant | 0.0026204 | 0.0018765 | 1.396437 | 0.1635358 |
Ljung Box test for autocorrelation of residuals
| .model | lb_stat | lb_pvalue |
|---|---|---|
| ARIMA(quantity) | 16.57448 | 0.084326 |
Model testing
Weekly data
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE |
|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | 0.2857800 | 0.46890 | 0.28578 | 19.2700 | 19.270 | 0.39684 |
| ETS(quantity ~ season(method = “N”)) | Test | 0.2930300 | 0.47409 | 0.29303 | 19.9170 | 19.917 | 0.40691 |
| FASSTER(quantity ~ trend(1)) | Test | -0.1147500 | 0.38994 | 0.35428 | -17.4630 | 29.439 | 0.49195 |
| prophet(quantity) | Test | 0.0088599 | 0.40518 | 0.28532 | -6.4686 | 21.178 | 0.39620 |
| SNAIVE(quantity) | Test | 0.3333300 | 0.81650 | 0.66667 | 25.0000 | 58.333 | 0.92573 |
Daily data
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE |
|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | 0.181280 | 0.34152 | 0.18128 | Inf | Inf | 1.3962 |
| ETS(quantity ~ season(method = “A”)) | Test | -0.042226 | 0.28420 | 0.18607 | -Inf | Inf | 1.4331 |
| FASSTER(quantity ~ trend(1) + fourier(7)) | Test | -0.081532 | 0.29093 | 0.22693 | -Inf | Inf | 1.7478 |
| prophet(quantity ~ season(7)) | Test | -0.052164 | 0.28547 | 0.20376 | -Inf | Inf | 1.5694 |
| SNAIVE(quantity ~ lag(“week”)) | Test | -0.047619 | 0.43644 | 0.19048 | -Inf | Inf | 1.4671 |
Cross validation
Cross validated accuracy for a variety of models using weekly data.
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE | ACF1 |
|---|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | -0.0075191 | 1.084065 | 0.7801328 | -Inf | Inf | 1.083293 | -0.0314451 |
| ETS(quantity ~ season(method = “N”)) | Test | 0.0083423 | 1.077461 | 0.7662528 | -Inf | Inf | 1.064019 | -0.0501597 |
| FASSTER(quantity ~ trend(1)) | Test | -0.0477061 | 1.151219 | 0.8402641 | -Inf | Inf | 1.166792 | 0.0617464 |
| prophet(quantity) | Test | -0.1224827 | 1.084903 | 0.8279418 | -Inf | Inf | 1.149681 | -0.0282379 |
| SNAIVE(quantity) | Test | -0.0833333 | 1.443376 | 1.0416667 | -Inf | Inf | 1.446459 | -0.0527453 |
Cross validation- daily
Cross validated accuracy for a variety of models using daily data.
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE | ACF1 |
|---|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | 0.1719968 | 0.4660033 | 0.1752919 | NaN | Inf | 1.402975 | 0.0022768 |
| ETS(quantity ~ season(method = “A”)) | Test | 0.0523478 | 0.4336203 | 0.2286735 | NaN | Inf | 1.830222 | -0.0152852 |
| FASSTER(quantity ~ trend(1) + fourier(7)) | Test | 0.0782281 | 0.4285844 | 0.2167827 | -Inf | Inf | 1.735053 | -0.0204113 |
| prophet(quantity ~ season(7)) | Test | 0.0368933 | 0.4246549 | 0.2472935 | -Inf | Inf | 1.979250 | -0.0197295 |
| SNAIVE(quantity ~ lag(“week”)) | Test | 0.0238095 | 0.5976143 | 0.3095238 | -Inf | Inf | 2.477320 | -0.0668105 |
Site B
Seasonality
Week
Year
Raw data
Detail of data
Weekly totals
Detail of weekly totals
Residuals of STL model- raw data and weekly totals
Simple exponential smoothing
| .model | term | estimate |
|---|---|---|
| ETS(quantity ~ season(method = “N”)) | alpha | 0.0510261 |
| ETS(quantity ~ season(method = “N”)) | l | 0.6459055 |
Ljung Box test for autocorrelation of residuals
| .model | lb_stat | lb_pvalue |
|---|---|---|
| ETS(quantity ~ season(method = “N”)) | 35.51043 | 0.0001021 |
ARIMA
| .model | term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|---|
| ARIMA(quantity) | ar1 | 1.1085028 | 0.1568118 | 7.0689995 | 0.0000000 |
| ARIMA(quantity) | ar2 | -0.4439474 | 0.2239199 | -1.9826172 | 0.0482493 |
| ARIMA(quantity) | ma1 | -1.2208366 | 0.1353474 | -9.0200206 | 0.0000000 |
| ARIMA(quantity) | ma2 | 0.6463738 | 0.2013875 | 3.2096017 | 0.0014614 |
| ARIMA(quantity) | sar1 | -0.4753740 | 1.3922863 | -0.3414341 | 0.7329968 |
| ARIMA(quantity) | sma1 | 0.5272700 | 1.3715643 | 0.3844296 | 0.7009107 |
| ARIMA(quantity) | constant | 0.3615233 | 0.0356792 | 10.1325938 | 0.0000000 |
Ljung Box test for autocorrelation of residuals
| .model | lb_stat | lb_pvalue |
|---|---|---|
| ARIMA(quantity) | 23.10871 | 0.0103524 |
Model testing
Weekly data
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE |
|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | 0.049325 | 0.51020 | 0.49213 | -Inf | Inf | 0.49959 |
| ETS(quantity ~ season(method = “N”)) | Test | -0.018531 | 0.47177 | 0.43827 | -Inf | Inf | 0.44491 |
| FASSTER(quantity ~ trend(1)) | Test | 0.507720 | 0.69282 | 0.61368 | -Inf | Inf | 0.62298 |
| prophet(quantity) | Test | 0.298750 | 0.57032 | 0.55387 | -Inf | Inf | 0.56226 |
| SNAIVE(quantity) | Test | 0.333330 | 0.81650 | 0.66667 | -Inf | Inf | 0.67677 |
Daily data
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE |
|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | 0.0141270 | 0.32413 | 0.19897 | -Inf | Inf | 1.04670 |
| ETS(quantity ~ season(method = “A”)) | Test | 0.0241040 | 0.31001 | 0.18325 | NaN | Inf | 0.96402 |
| FASSTER(quantity ~ trend(1) + fourier(7)) | Test | -0.0630860 | 0.31443 | 0.24194 | -Inf | Inf | 1.27270 |
| prophet(quantity ~ season(7)) | Test | 0.0084737 | 0.30592 | 0.18700 | NaN | Inf | 0.98370 |
| SNAIVE(quantity ~ lag(“week”)) | Test | -0.0238100 | 0.51177 | 0.26190 | -Inf | Inf | 1.37780 |
Cross validation
Cross validated accuracy for a variety of models using weekly data.
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE | ACF1 |
|---|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | -0.0924686 | 1.029245 | 0.8001087 | -Inf | Inf | 0.8122315 | 0.0072850 |
| ETS(quantity ~ season(method = “N”)) | Test | -0.1648498 | 1.146186 | 0.9063780 | -Inf | Inf | 0.9201110 | 0.1682406 |
| FASSTER(quantity ~ trend(1)) | Test | -0.0580629 | 1.186955 | 0.8890300 | -Inf | Inf | 0.9025001 | 0.2119620 |
| prophet(quantity) | Test | 0.0939788 | 1.081651 | 0.7825832 | -Inf | Inf | 0.7944405 | 0.0620541 |
| SNAIVE(quantity) | Test | 0.0000000 | 1.457738 | 1.0000000 | -Inf | Inf | 1.0151515 | 0.2843137 |
Cross validation- daily
Cross validated accuracy for a variety of models using daily data.
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE | ACF1 |
|---|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | -0.0582267 | 0.2207598 | 0.1433771 | -Inf | Inf | 0.7468548 | -0.0512831 |
| ETS(quantity ~ season(method = “A”)) | Test | -0.0648977 | 0.2180195 | 0.1415660 | NaN | Inf | 0.7374211 | -0.0306467 |
| FASSTER(quantity ~ trend(1) + fourier(7)) | Test | 0.0639730 | 0.2168716 | 0.1039410 | NaN | Inf | 0.5414313 | -0.0294029 |
| prophet(quantity ~ season(7)) | Test | -0.0749898 | 0.2173256 | 0.1490010 | NaN | Inf | 0.7761499 | -0.0176000 |
| SNAIVE(quantity ~ lag(“week”)) | Test | 0.0476190 | 0.2182179 | 0.0476190 | 100 | 100 | 0.2480489 | -0.0511905 |
Site C
Seasonality
Week
Year
Raw data
Detail of data
Weekly totals
Detail of weekly totals
Residuals of STL model- raw data and weekly totals
Simple exponential smoothing
| .model | term | estimate |
|---|---|---|
| ETS(quantity ~ season(method = “N”)) | alpha | 0.0550134 |
| ETS(quantity ~ season(method = “N”)) | l | 4.2467197 |
Ljung Box test for autocorrelation of residuals
| .model | lb_stat | lb_pvalue |
|---|---|---|
| ETS(quantity ~ season(method = “N”)) | 87.48554 | 0 |
ARIMA
| .model | term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|---|
| ARIMA(quantity) | ar1 | -0.9658588 | 0.0355692 | -27.1543820 | 0.0000000 |
| ARIMA(quantity) | ma1 | 0.0059256 | 0.0441196 | 0.1343079 | 0.8932412 |
| ARIMA(quantity) | ma2 | -0.8966608 | 0.0426436 | -21.0268672 | 0.0000000 |
| ARIMA(quantity) | sar1 | 0.0653839 | 0.0596098 | 1.0968645 | 0.2735028 |
| ARIMA(quantity) | sar2 | 0.1455756 | 0.0702639 | 2.0718414 | 0.0390591 |
| ARIMA(quantity) | constant | -0.0100556 | 0.0123544 | -0.8139305 | 0.4162735 |
Ljung Box test for autocorrelation of residuals
| .model | lb_stat | lb_pvalue |
|---|---|---|
| ARIMA(quantity) | 83.59398 | 0 |
Model testing
Weekly data
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE |
|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | 0.64151 | 2.4227 | 1.7647 | -Inf | Inf | 0.79338 |
| ETS(quantity ~ season(method = “N”)) | Test | 0.48847 | 2.4071 | 1.7184 | -Inf | Inf | 0.77256 |
| FASSTER(quantity ~ trend(1)) | Test | 1.62290 | 2.8617 | 2.0965 | -Inf | Inf | 0.94257 |
| prophet(quantity) | Test | 0.61216 | 2.5062 | 2.0342 | -Inf | Inf | 0.91454 |
| SNAIVE(quantity) | Test | 0.16667 | 3.1885 | 2.8333 | -Inf | Inf | 1.27380 |
Daily data
## Warning in sqrt(diag(best$var.coef)): NaNs produced
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE |
|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | 0.105980 | 0.74299 | 0.42298 | -Inf | Inf | 0.67971 |
| ETS(quantity ~ season(method = “A”)) | Test | 0.034746 | 0.71316 | 0.40522 | NaN | Inf | 0.65117 |
| FASSTER(quantity ~ trend(1) + fourier(7)) | Test | -0.269390 | 0.78786 | 0.55025 | -Inf | Inf | 0.88424 |
| prophet(quantity ~ season(7)) | Test | 0.053329 | 0.74303 | 0.47984 | NaN | Inf | 0.77109 |
| SNAIVE(quantity ~ lag(“week”)) | Test | 0.023810 | 0.74001 | 0.40476 | -Inf | Inf | 0.65044 |
Cross validation
Cross validated accuracy for a variety of models using weekly data.
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE | ACF1 |
|---|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | -0.0615136 | 1.650035 | 1.305759 | -Inf | Inf | 0.5851895 | -0.1543366 |
| ETS(quantity ~ season(method = “N”)) | Test | 0.0265369 | 1.538735 | 1.189461 | -Inf | Inf | 0.5330693 | -0.2000109 |
| FASSTER(quantity ~ trend(1)) | Test | 0.0922926 | 1.721218 | 1.435999 | -Inf | Inf | 0.6435579 | -0.0389326 |
| prophet(quantity) | Test | 0.7740712 | 1.798016 | 1.364955 | -Inf | Inf | 0.6117188 | -0.1245546 |
| SNAIVE(quantity) | Test | 0.2708333 | 2.155419 | 1.645833 | -Inf | Inf | 0.7375975 | -0.1637894 |
Cross validation- daily
Cross validated accuracy for a variety of models using daily data.
## Warning in sqrt(diag(best$var.coef)): NaNs produced| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE | ACF1 |
|---|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | -0.1017775 | 0.4850811 | 0.4269597 | -Inf | Inf | 0.6775128 | 0.0097210 |
| ETS(quantity ~ season(method = “A”)) | Test | -0.0863789 | 0.4413631 | 0.3468492 | -Inf | Inf | 0.5503909 | -0.0543017 |
| FASSTER(quantity ~ trend(1) + fourier(7)) | Test | -0.3537661 | 0.6193490 | 0.5071441 | -Inf | Inf | 0.8047519 | -0.0021417 |
| prophet(quantity ~ season(7)) | Test | -0.0310719 | 0.5113278 | 0.4371493 | NaN | Inf | 0.6936819 | 0.0018050 |
| SNAIVE(quantity ~ lag(“week”)) | Test | -0.1904762 | 0.5773503 | 0.3333333 | -Inf | Inf | 0.5289436 | 0.1802981 |
Drug D
Site A
Seasonality
Week
Year
Raw data
Detail of data
Weekly totals
Detail of weekly totals
Residuals of STL model- raw data and weekly totals
Simple exponential smoothing
| .model | term | estimate |
|---|---|---|
| ETS(quantity ~ season(method = “N”)) | alpha | 0.1177532 |
| ETS(quantity ~ season(method = “N”)) | l | 7.9912120 |
Ljung Box test for autocorrelation of residuals
| .model | lb_stat | lb_pvalue |
|---|---|---|
| ETS(quantity ~ season(method = “N”)) | 35.48464 | 0.0001032 |
ARIMA
| .model | term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|---|
| ARIMA(quantity) | ma1 | -0.8780575 | 0.0323965 | -27.1034327 | 0.0000000 |
| ARIMA(quantity) | sar1 | 0.0354841 | 0.0786125 | 0.4513799 | 0.6520441 |
Ljung Box test for autocorrelation of residuals
| .model | lb_stat | lb_pvalue |
|---|---|---|
| ARIMA(quantity) | 36.34574 | 7.34e-05 |
Model testing
Weekly data
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE |
|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | 3.9053 | 11.142 | 5.1743 | -Inf | Inf | 0.49484 |
| ETS(quantity ~ season(method = “N”)) | Test | 3.7817 | 11.099 | 5.2566 | -Inf | Inf | 0.50272 |
| FASSTER(quantity ~ trend(1)) | Test | 4.6667 | 11.431 | 4.6667 | -Inf | Inf | 0.44630 |
| prophet(quantity) | Test | -4.6423 | 10.117 | 9.3066 | -Inf | Inf | 0.89004 |
| SNAIVE(quantity) | Test | 4.6667 | 11.431 | 4.6667 | 100 | 100 | 0.44630 |
Daily data
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE |
|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | 0.63313 | 4.3154 | 0.69861 | -Inf | Inf | 0.42239 |
| ETS(quantity ~ season(method = “A”)) | Test | 0.62472 | 4.3894 | 1.23170 | NaN | Inf | 0.74473 |
| FASSTER(quantity ~ trend(1) + fourier(7)) | Test | 0.37721 | 4.3587 | 1.29820 | NaN | Inf | 0.78492 |
| prophet(quantity ~ season(7)) | Test | 0.40451 | 4.3524 | 1.32570 | NaN | Inf | 0.80155 |
| SNAIVE(quantity ~ lag(“week”)) | Test | 0.66667 | 4.3205 | 0.66667 | 100 | 100 | 0.40308 |
Cross validation
Cross validated accuracy for a variety of models using weekly data.
## Warning in sqrt(diag(best$var.coef)): NaNs produced
## Warning in sqrt(diag(best$var.coef)): NaNs produced| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE | ACF1 |
|---|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | -2.1289946 | 11.38355 | 8.513096 | -Inf | Inf | 0.8059335 | 0.5991547 |
| ETS(quantity ~ season(method = “N”)) | Test | -2.6259821 | 12.95669 | 9.054866 | -Inf | Inf | 0.8572228 | 0.6357883 |
| FASSTER(quantity ~ trend(1)) | Test | -2.0161909 | 13.80218 | 8.287724 | -Inf | Inf | 0.7845976 | 0.6142209 |
| prophet(quantity) | Test | 3.1673360 | 10.36205 | 6.322520 | NaN | Inf | 0.5985520 | 0.5217602 |
| SNAIVE(quantity) | Test | 0.3666667 | 12.70827 | 5.300000 | -Inf | Inf | 0.5017502 | 0.0532605 |
Cross validation- daily
Cross validated accuracy for a variety of models using daily data.
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE | ACF1 |
|---|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | -0.0893772 | 0.0893787 | 0.0893772 | -Inf | Inf | 0.0525763 | 0.0363889 |
| ETS(quantity ~ season(method = “A”)) | Test | -0.0719456 | 0.7260574 | 0.5607913 | NaN | Inf | 0.3298861 | 0.2397081 |
| FASSTER(quantity ~ trend(1) + fourier(7)) | Test | 0.0982023 | 0.7376932 | 0.6125365 | NaN | Inf | 0.3603253 | 0.2392553 |
| prophet(quantity ~ season(7)) | Test | -0.4127489 | 0.8614791 | 0.7291816 | NaN | Inf | 0.4289418 | 0.2948788 |
| SNAIVE(quantity ~ lag(“week”)) | Test | 0.0000000 | 0.0000000 | 0.0000000 | NaN | NaN | 0.0000000 | NaN |
Site B
Seasonality
Week
Year
Raw data
Detail of data
Weekly totals
Detail of weekly totals
Residuals of STL model- raw data and weekly totals
Simple exponential smoothing
| .model | term | estimate |
|---|---|---|
| ETS(quantity ~ season(method = “N”)) | alpha | 0.0807574 |
| ETS(quantity ~ season(method = “N”)) | l | 17.8629306 |
Ljung Box test for autocorrelation of residuals
| .model | lb_stat | lb_pvalue |
|---|---|---|
| ETS(quantity ~ season(method = “N”)) | 26.27242 | 0.0033906 |
ARIMA
| .model | term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|---|
| ARIMA(quantity) | ar1 | -0.1995096 | 0.0747021 | -2.670737 | 0.0079493 |
| ARIMA(quantity) | ma1 | -0.8003094 | 0.0616738 | -12.976498 | 0.0000000 |
Ljung Box test for autocorrelation of residuals
| .model | lb_stat | lb_pvalue |
|---|---|---|
| ARIMA(quantity) | 16.76456 | 0.0797388 |
Model testing
Weekly data
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE |
|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | 11.6770 | 18.153 | 13.893 | -Inf | Inf | 0.43867 |
| ETS(quantity ~ season(method = “N”)) | Test | 7.0046 | 15.509 | 13.833 | -Inf | Inf | 0.43677 |
| FASSTER(quantity ~ trend(1)) | Test | 13.7510 | 19.508 | 13.833 | -Inf | Inf | 0.43677 |
| prophet(quantity) | Test | 9.9557 | 15.389 | 12.851 | NaN | Inf | 0.40574 |
| SNAIVE(quantity) | Test | 4.5000 | 19.803 | 14.167 | -Inf | Inf | 0.44730 |
Daily data
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE |
|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | 1.7259 | 8.3257 | 3.3840 | -Inf | Inf | 0.64965 |
| ETS(quantity ~ season(method = “A”)) | Test | 2.1609 | 8.6052 | 4.3626 | NaN | Inf | 0.83752 |
| FASSTER(quantity ~ trend(1) + fourier(7)) | Test | 1.9376 | 8.5445 | 4.4014 | NaN | Inf | 0.84498 |
| prophet(quantity ~ season(7)) | Test | 1.7174 | 8.5985 | 4.5187 | NaN | Inf | 0.86749 |
| SNAIVE(quantity ~ lag(“week”)) | Test | 2.6429 | 8.5649 | 2.6429 | 100 | 100 | 0.50737 |
Cross validation
Cross validated accuracy for a variety of models using weekly data.
## Warning in sqrt(diag(best$var.coef)): NaNs produced
## Warning in sqrt(diag(best$var.coef)): NaNs produced| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE | ACF1 |
|---|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | 3.909257 | 16.10149 | 12.45077 | NaN | Inf | 0.3931205 | 0.1871885 |
| ETS(quantity ~ season(method = “N”)) | Test | 1.404502 | 15.58327 | 12.80260 | -Inf | Inf | 0.4042292 | 0.2580917 |
| FASSTER(quantity ~ trend(1)) | Test | 4.778155 | 16.04366 | 11.23543 | -Inf | Inf | 0.3547474 | 0.2507581 |
| prophet(quantity) | Test | 3.947609 | 21.85388 | 15.53651 | NaN | Inf | 0.4905495 | 0.5759967 |
| SNAIVE(quantity) | Test | 1.583333 | 29.88101 | 14.54167 | -Inf | Inf | 0.4591384 | 0.1209607 |
Cross validation- daily
Cross validated accuracy for a variety of models using daily data.
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE | ACF1 |
|---|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | -1.5823089 | 1.582480 | 1.582309 | -Inf | Inf | 0.2973949 | 0.8575486 |
| ETS(quantity ~ season(method = “A”)) | Test | -1.1804705 | 2.455482 | 2.242985 | NaN | Inf | 0.4215688 | 0.4013534 |
| FASSTER(quantity ~ trend(1) + fourier(7)) | Test | 0.6727588 | 2.271434 | 1.665238 | NaN | Inf | 0.3129813 | 0.3924931 |
| prophet(quantity ~ season(7)) | Test | -1.4829513 | 2.628925 | 2.306418 | NaN | Inf | 0.4334912 | 0.3890467 |
| SNAIVE(quantity ~ lag(“week”)) | Test | 0.0000000 | 0.000000 | 0.000000 | NaN | NaN | 0.0000000 | NaN |
Site C
Seasonality
Week
Year
Raw data
Detail of data
Weekly totals
Detail of weekly totals
Residuals of STL model- raw data and weekly totals
Simple exponential smoothing
| .model | term | estimate |
|---|---|---|
| ETS(quantity ~ season(method = “N”)) | alpha | 0.0532616 |
| ETS(quantity ~ season(method = “N”)) | l | 107.9514229 |
Ljung Box test for autocorrelation of residuals
| .model | lb_stat | lb_pvalue |
|---|---|---|
| ETS(quantity ~ season(method = “N”)) | 54.70743 | 0 |
ARIMA
| .model | term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|---|
| ARIMA(quantity) | ar1 | -0.8631315 | 0.0787298 | -10.9632122 | 0.0000000 |
| ARIMA(quantity) | ma1 | 0.0236562 | 0.0936657 | 0.2525604 | 0.8007671 |
| ARIMA(quantity) | ma2 | -0.7615099 | 0.0822297 | -9.2607650 | 0.0000000 |
| ARIMA(quantity) | ma3 | -0.1759554 | 0.0590797 | -2.9782710 | 0.0031161 |
| ARIMA(quantity) | sar1 | 0.0159874 | 0.0590524 | 0.2707316 | 0.7867688 |
| ARIMA(quantity) | sar2 | 0.1144626 | 0.0674947 | 1.6958748 | 0.0908643 |
Ljung Box test for autocorrelation of residuals
| .model | lb_stat | lb_pvalue |
|---|---|---|
| ARIMA(quantity) | 37.74725 | 4.2e-05 |
Model testing
Weekly data
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE |
|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | -37.0820 | 39.045 | 37.0820 | -Inf | Inf | 0.68225 |
| ETS(quantity ~ season(method = “N”)) | Test | -41.1820 | 42.508 | 41.1820 | -Inf | Inf | 0.75768 |
| FASSTER(quantity ~ trend(1)) | Test | -6.4169 | 12.250 | 12.0560 | -Inf | Inf | 0.22180 |
| prophet(quantity) | Test | -5.6451 | 12.873 | 9.8279 | NaN | Inf | 0.18082 |
| SNAIVE(quantity) | Test | -28.0000 | 48.497 | 37.3330 | -Inf | Inf | 0.68687 |
Daily data
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE |
|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | 2.27100 | 9.7607 | 2.2710 | Inf | Inf | 0.17621 |
| ETS(quantity ~ season(method = “A”)) | Test | -3.40430 | 11.0670 | 7.0533 | NaN | Inf | 0.54725 |
| FASSTER(quantity ~ trend(1) + fourier(7)) | Test | -0.96906 | 11.7240 | 8.0877 | NaN | Inf | 0.62751 |
| prophet(quantity ~ season(7)) | Test | -2.58400 | 11.9220 | 8.2236 | NaN | Inf | 0.63805 |
| SNAIVE(quantity ~ lag(“week”)) | Test | 2.00000 | 9.6609 | 2.0000 | 100 | 100 | 0.15518 |
Cross validation
Cross validated accuracy for a variety of models using weekly data.
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE | ACF1 |
|---|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | -3.8681462 | 37.93263 | 32.35715 | -Inf | Inf | 0.5942380 | 0.3955366 |
| ETS(quantity ~ season(method = “N”)) | Test | -3.9285852 | 37.50104 | 31.85796 | -Inf | Inf | 0.5850705 | 0.3922062 |
| FASSTER(quantity ~ trend(1)) | Test | 0.0330934 | 34.85186 | 27.56318 | -Inf | Inf | 0.5061970 | 0.3145006 |
| prophet(quantity) | Test | 5.5815139 | 41.67960 | 32.01539 | NaN | Inf | 0.5879616 | 0.4212981 |
| SNAIVE(quantity) | Test | -3.5000000 | 59.67132 | 44.33333 | -Inf | Inf | 0.8141803 | 0.4159235 |
Cross validation- daily
Cross validated accuracy for a variety of models using daily data.
| .model | .type | ME | RMSE | MAE | MPE | MAPE | MASE | ACF1 |
|---|---|---|---|---|---|---|---|---|
| ARIMA(quantity) | Test | -40.378875 | 41.384168 | 40.378875 | -Inf | Inf | 3.0791736 | 0.0041697 |
| ETS(quantity ~ season(method = “A”)) | Test | -4.766195 | 9.703612 | 7.659677 | -Inf | Inf | 0.5841043 | -0.0681954 |
| FASSTER(quantity ~ trend(1) + fourier(7)) | Test | -11.052605 | 15.195554 | 13.074809 | -Inf | Inf | 0.9970463 | 0.0831263 |
| prophet(quantity ~ season(7)) | Test | -3.372669 | 11.116702 | 8.864495 | NaN | Inf | 0.6759802 | 0.0776819 |
| SNAIVE(quantity ~ lag(“week”)) | Test | -5.333333 | 22.861904 | 10.666667 | -Inf | Inf | 0.8134084 | -0.1200754 |